Alfonso Caiazzo, Wolfgang Dreyer, Derk Frerichs, Jürgen Fuhrmann, René Kehl, Zahra Lakdawala, Alexander Linke, Christian Merdon, Baptiste Moreau, Ondřej Pártl, Hang Si, Holger Stephan, Timo Streckenbach, Petr Vágner, Ulrich Wilbrandt
APPRENTICESHIP TRAINING: Mathematical-Technical Software Developer
Apprentices: Mihaela Karcheva, Leo Markmann
Instructor: Holger Stephan, Training Officer: Timo Streckenbach
Contact: Phone: +49 30 20372 566, Fax: +49 30 20372 303
The mathematical modeling of a large number of scientific and technical problems leads to systems of differential equations describing the interactions of temporal and spatial variations of the considered physical processes. If the spatial variations are irrelevant, the processes are described by ordinary differential equations (ODEs). The connection with additional algebraic equations results in differential-algebraic equations (DAEs). DAEs are used to model, e.g., electrical networks and chemical plants. If the spatial structure of the process is important, partial differential equations (PDEs) are utilized as models. PDEs describe problems from structural analysis, from fluid mechanics, electro-magnetic problems, or particle diffusion. In general, it is not possible to solve the equations arising from applications in closed form. Numerical methods have to be used to obtain approximate solutions.
The research group develops, analyzes, and implements modern numerical methods for the solution of systems of PDEs and DAEs. An essential aspect of the studied methods is their practicability in applications.
The emphasis of the research activities is on:
- finite element and finite volume methods for the spatial discretization of PDEs,
- implicit schemes for their temporal discretization,
- numerical methods for systems of DAEs and resulting questions of numerical linear algebra and
- computational geometry (grid generation).
- Partial Differential Equations
- Laser Dynamics
- Numerical Mathematics and Scientific Computing
- Nonlinear Optimization and Inverse Problems
- Interacting Random Systems
- Stochastic Algorithms and Nonparametric Statistics
- Thermodynamic Modeling and Analysis of Phase Transitions
- Nonsmooth Variational Problems and Operator Equations